We had radon issues here (down in Devon), when we renovated we had to put down a particular type of membrane and a sump below the membrane which vents externally. However the family had been living here for 100 years beforehand with no issues, so I don't think it is a massive issue, and I think the materials cost us an extra couple of hundred quid to sort out, but can't imagine you would have to do anything retrospectively.
We had radon issues here (down in Devon), when we renovated we had to put down a particular type of membrane and a sump below the membrane which vents externally. However the family had been living here for 100 years beforehand with no issues, so I don't think it is a massive issue, and I think the materials cost us an extra couple of hundred quid to sort out, but can't imagine you would have to do anything retrospectively.